I'm pretty sure even though car A was there first, car B has right of way. But it would be nice for car B to wait so that both cars can turn during the gap. If I am car B, I try to let car A out first if there's space for us both. If not, I turn and poor car A has to sit there some more....

I always thought the car that doesnt have to cross the road to the otherside gets priority even if arrived at junction last. Cars on the main road gets priortity full stop to side roads. Hope that helps. Not sure what the highway code says. Might be worth checking.

With 4 lanes though, if car B decided to be nice and hang back, would they not possibly be at risk of causing an accident by letting car A go first as other cars coming up behind may not see what is going on?

If car B is in the right hand lane of their side of the road and flashes car A to go first and car A joins that lane in front of B rather than going far left, then there can't be an accident, even if someone is passing car B on the left. However if it's a road with a central refuge and car B is in that and not sitting in a lane then yes, you're right about it potentially causing an accident if car A goes without checking. But anytime anybody "lets you out" against normal priorities it is your responsibility to check it's safe not just accept.

SpottedZebra I was getting desperate as the junction has been like this for a few weeks now, since they closed the adjacent traffic-light-controlled road for works (and will be for 9 bloody months more), and often when I have to turn in or out (minimum twice a day) the other person seems to have a different idea to me. When I am Car B I hang back and be nice, but then the Car A person sometimes takes ages to wake up and realise what I'm doing, so I lose my right turn gap. When I am Car A, I sometimes get a Car B person waving me out, but sometimes not.

Now I know Car B has priority I will stop giving them death ray glares if they don't let me out, and consider it a nice bonus if they do. Will still try to be nice to Car As when it's the other way round though, as it can take up to 5 minutes to get out otherwise.

Car B has priority. And I have to admit it annoys me a bit if I'm driving car A and the driver of car B flashes me to go. It's simpler if the person with priority just goes first, without a lot of "You go." "No, you go." "No honestly, I'd be delighted if you go." Etc.

Unless there's insufficient space for car B to pass car A after turning into the minor road, in which case car B really should yield to car A.